 Temporal coherence from crossed beams

Split one stationary scalar optical field into equal copies travelling at right angles with common transverse linear polarization. For wavevectors $k(\hat{\mathbf{x}}\pm \hat{\mathbf{y}})/\sqrt{2}$, the relative geometric delay is $\sqrt{2}y/c$ in vacuum, while the delay on the $x$ bisector is zero. The electric-field intensity convention gives the displayed pattern and $I(x)=2I_0$. The mean Poynting vector points along $+x$, with magnitude $I(y)/\sqrt{2}$ in that convention. A transverse detector can record the $y$ profile if it resolves the period $\lambda /\sqrt{2}$; a longitudinal $x$ profile is not a transverse camera image.